MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Consider the curves p(x)=x2+2x+1 and q(x)=2x+5 on the closed interval [−3,2].
(a) Show algebraically that p and q intersect at exactly two points and find their x-coordinates.
(b) Determine which function is greater on the interval [−3,2] except at the points of intersection. Support your conclusion with analytic evidence.
(c) Calculate the exact value of the area of the finite region enclosed by the graphs of p and q and the vertical lines x=−3 and x=2.
(d) Interpret the sign of your integrand in part (c) in terms of the geometric meaning of “top minus bottom.”